A-LevelMathematicsTrigonometry9709/33 · May/June 2019 · Q77 Marks
The curve y = sin(x + (1/3)π) cos x has two stationary points in the interval 0 ≤ x ≤ π.
- (i)Find dy/dx[2]
- (ii)By considering the formula for cos(A + B), show that, at the stationary points on the curve, cos(2x + (1/3)π) = 0.[2]
- (iii)Hence find the exact x-coordinates of the stationary points.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Use product rule
- [A1] Obtain correct derivative in any form
- [M1] Equate derivative to zero and use correct cos(A + B) formula
- [A1] Obtain the given equation
- [M1] Use correct method to solve for x
- [A1] Obtain answer, e.g. x = (1/12)π
- [A1] Obtain second answer, e.g. x = (7/12)π, and no other
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